Fluid Salients and the Formation of Beach Cusps
Michael A.
Gorycki, Ph.D.
July, 2008 ABSTRACT In my earlier website I discussed
the importance of fluid salients to the structuring of moving fluids in a
number of natural and laboratory phenomena. The mechanism appears in a variety
of guises, depending on the conditions of its development, but in the simplest
case the broad leading edge of a moving fluid, impeded by its substrate,
overrolls, thins, and extends axially (laterally). To relieve the resulting
axial compression generated, a series of evenly spaced salients, with
intervening retarded zones, forms at right angles to that edge. It is these
parabolic salients, produced as a wave ascends the beach face, that I feel are
responsible for the initiation, formation, and maintenance of a beach cusp
series. Included in the present web site are additional comments on the role of
fluid salients in the formation of beach cusps. INTRODUCTION Palmer first described beach
cusps in 1834, but assuredly, they have been contemplated for as long as people
have observed the action of waves on the beach face. It is an explanation of
their periodicity that has provided a kind of Holy Grail sought after by beach
morphologists for almost a century, for as Johnson (1919, p. 457) states,
“Among the minor forms of the shore zone none has proved more puzzling than the
cuspate deposits of beach material built by wave action along the foreshore.
Sand, gravel, or coarse cobblestones are heaped together in rather uniformly
spaced ridges which trend at right angles to the sea margin, tapering out to a
point near the water's edge. These 'beach cusps' have attracted the attention
of many students.” Having once observed that the
leading edge of a small amount of water sloshed across the bottom of a small
tilted tray forms a series of salients, it immediately became clear that this
could be the mechanism for the formation of evenly spaced beach cusps (Gorycki,
1973). I later constructed a large rocking trough to display this phenomenon on
a larger scale, and a physical model that demonstrates a similar deformation of
a thin rubber cylinder by rolling it between two pieces of plate glass. After
some experimentation, field study and a review of published research, I still
find that the fluid salient mechanism, supported by its appearance in a
disparate variety of natural phenomena offers the most viable explanation for
the formation of beach cusps (see figures 1-7 in my earlier web site). [1] http://www.geocities.com/magsalients/ The literature is replete with a
variety of observations related to cusp phenomena and, for convenience of
discussion, I have grouped these works under several headings. They are: BEACH CUSPS AND
RIP CURRENTS BEACH CUSPS AND
NEARSHORE CIRCULATION CELLS BEACH CUSPS AND
EDGE WAVES BEACH CUSPS AND
THE SELF-ORGANIZATION MODEL BEACH CUSPS AND RIP CURRENTS Much has been written about field and laboratory observations
concerning beach cusp series, and research has generated a number of theories.
Often, however, papers either avoid discussion of a mechanism that provides for
the even spacing of beach cusps, or suggest that further analysis is necessary
to solve the problem of their occurrence. In my paper (Gorycki, 1973), I
suggested that as waves initially encounter the beach face, they can develop
evenly spaced salients separated by zones of retarded flow. This structuring
apparently is due to overrolling of the plunging wave orbit, with thinning and
axial extension of the wave in a direction parallel to the shoreline as the
wave begins to “feel bottom”, and is based on my rocking trough observations
(Fig. 1) and the physical model (Fig. 2). Fig.
1. A sheet of water is shown overriding the floor of a large rocking trough.
Evenly spaced, parabolic water salients with intervening zones of retarded flow
are formed, based on the forward velocity and speed of overrolling. No
influence of the side walls on any salient series is apparent. Scale line is 10
cm long; arrow shows direction of water
motion [1]. Not all wave regimes produce
cusps. Sufficient lateral extension, based on overrolling and speed of the
uprush, must be generated to produce the distortion resulting in salient
formation. In the rubber cylinder model sufficient distortion must be generated
to produce the salients as the cylinder is rolled and extended, but without any
velocity requirements. As discussed in my earlier web site [1] the mechanism
may also be involved during plate tectonics by operating, over time, at the
edges of overriding lithospheric plates to produce the familiar arc-like
patterns. The even spacing of tectonic arcs on the west coasts of North and
South America, from the Aleutians to Peru, suggest this. In places where the
mechanism is interrupted, such as at the southern end of Chile, the arcs end,
thus providing that country with a straight coastline. This straight portion
may also be seen at either end of the rubber cylinder model (Fig. 2). Fig.
2. A physical model of salients and zones of retarded flow, formed by rolling a
thin rubber cylinder between two glass plates [1]. Pressure on the cylinder
produces axial extension, which generates the salients. The speed of forward
motion of the upper plate is not a consideration here. The flattened cylinder
is about 1 mm wide. Motion of the upper plate is perpendicular to the
length of the cylinder, but a similar pattern is produced if the upper plate is
moved at an acute angle to the perpendicular. The former situation
suggests cusp formation produced by waves moving directly toward the shoreline,
the latter, by waves approaching the shoreline at an angle but which are also
capable of producing a cusp series. If the upper plate is moved parallel
to the cylinder’s length, a similar pattern develops, but it is based on a different
internal distortion of the cylinder [1]. It is obvious that a single wave train approaching
parallel to the shore would be considered most likely to generate and maintain
a beach cusp series. A single wave train approaching at a large angle to
the shore would not be conducive to development of the fluid salient mechanism
and would thus inhibit beach cusp formation. If two wave trains, each
approaching parallel to the shoreline were out of phase or they each exhibited
a different wavelength or amplitude, they would collectively produce waves of
irregular height, strength, and periodicity that could adversely affect the
formation or maintenance of a cusp series. However, even such a random sea
might also produce a beach cusp series.
Apparently, uniform wave height and strength is conducive, but not essential,
to cusp development and maintenance. Some waves in a series may aid in cusp
formation, others may have little, or no effect, and the damage done by still
others may subsequently be repaired by waves of the proper strength. Importantly, Evans (1938) provides further evidence for
cusp and bay initiation by describing the formation of a series of beach cusps
as the result of the action of a single wave. This abrupt structuring of the
beach face is also suggested by the image depicted below (Fig. 3). Fig.
3. One pass of water salients sweeping strewn sand, both forward and laterally
on the rocking trough floor, into parabolic streaks (Gorycki, 1973). On the
beach face, the apices of the parabolas represent salients transporting sand
shoreward to aid in cusp formation. The elongate limbs of the parabolas, formed
in the retarded portions of the salients by the lateral motion of the water,
would provide excavated sand carried seaward by backwash to deposit as
submarine deltas in the bays. The purpose of this model is to show that a
single wave moving across a surface is capable of forming salients and
producing an arrangement of evenly spaced sedimentary structures. Scale line
represents 20 cm; arrow shows direction of water motion [1]. Salients formed by such a wave might then deposit sand at
evenly spaced locations on the beach face to initiate cusp formation. More
importantly, each salient would then spread and move bilaterally from each
cusp, joining with spreading salients from adjacent cusps to return to the sea
and thus erode the bays that develop between cusps. The sediment derived from
the bays would then form submarine deltas seaward of the bays. The deltas and
associated return flow would then inhibit portions of the next approaching wave
of similar strength, thus segmenting it, so that the unretarded portions will
approach the beach face as salients centered on the cusps. As a consequence of
the action of a single wave, a series of cusps, bays, and deltas would be
initiated and then accentuated by continued action of a wave train and the
alignment of salients on cusps. Variation in salient spacing would be a
function of wave train velocity, amplitude, sediment roughness, water density
and viscosity, etc. However, it would be the operation of the fluid salient
mechanism that would be responsible for the even spacing in the cusp series and
provide for their development and maintenance.
As an aside, there is some
confusion in the literature with regard to water traveling across the beach
face, or foreshore portion, which is normally exposed to the action of the
swash. Swash (or uprush) is water moving up the beach face as the result of
breaking waves. Backrush (or backwash) is the broad seaward return of
swash on the beach face. Undertow, as its name implies, should be considered as
the return flow of submerged backrush on the beach face. Rip currents,
on the other hand, are relatively narrow, linear currents of return flow from
the beach face. Rip currents receive a great deal
of attention because they are dangerous and powerful enough to drag a swimmer
out to sea. Depending on the beach environment, rips can be far apart or
closely spaced and irregularly or (of interest here) evenly spaced. They are
also considered here because they are thought by some workers to be associated
with beach cusps. Rip currents can be formed in
several ways on a sandy beach and a general understanding of their formation is
appropriate at this point. The simplest situation involves waves which are
parallel to the shore and which move directly toward the beach. As waves break
on the beach face, it is obvious that a portion of their mass (the set-up) can
be supported above the general level of the sea by subsequent waves breaking in
the surf zone as well as by strong onshore winds. This unstable
condition at the shoreline is relieved by the formation of bi-directional
longshore currents that move parallel (and close) to the water's edge.
Longshore currents have zero velocity at their points of divergence,
which is located somewhere between two adjacent rip currents. A pair of converging
longshore currents move faster as they approach the rip location and one would
assume that they meet at a point where they are of identical strength,
sufficient energy, and where the slope of the beach face promotes a seaward
return. Their strength, location, and spacing are a function of the amount of
water pushed ashore. The converging longshore currents then merge to form a
feeder current that returns water directly seaward, extending beyond the
breaker zone as a rip current. I would suggest that an even spacing to the rips
results if wave conditions and a uniform beach face persist over a lengthy
section of the shoreline. Further seaward the rip current
will meet opposing wave motion (and the general mass of the sea) to form a
diffuse rip head (Shepard and Inman, 1951). I suggest that sediment plumes seen
in rip currents and heads may form offshore submarine deltas, possibly added to
by material from rip channels gouged out of the sea bottom. These deltas, in
combination with the rip heads and rip currents will oppose (in their
vicinities) those portions of subsequent incoming waves that will break early
at some distance from the beach. It is these portions of early-breaking waves
that cause the remainder of each incoming wave to be broken into large,
unhindered portions that reach the beach face and add to the longshore currents
so that the cycle may continue. In time, the channels and deltas formed will
become more defined and stabilized with regard to their locations on the beach.
It has been observed that once established, rip current locations can be stable
for months. [2] http://news.ufl.edu/2000/research/engineering/2000/
A variation of rip current
formation has incoming waves approaching the beach at a small angle. As a
function of that angle, a greater portion of one of a pair of longshore
currents will move upbeach along the water's edge in the same general direction
as the incoming waves. At a location where relative momentum slow a converging
pair sufficiently, they will merge and return to the sea as a rip current, but
at an angle to the water's edge (see figure 1, Inman and Guza, 1982). Possibly, if the angle of the incoming waves is very large, uni-directional longshore currents might be formed which return to the sea as rip currents, with spacings dependent on the set-up and the slope of the beach face. Another variation involves the
presence of an offshore bar, created in the surf zone, acting to contain and
channel the waters of the longshore currents. As water returns to the sea as a
rip current, a portion of the offshore bar must be breached, again, at an
apparent point of equal strength of converging longshore currents. Here too,
there is the possibility of the development of a submarine delta further
seaward a product of the sediment plume, and rip channel, current, and head. McKenzie (1958) noted that during
high-energy wave conditions rip currents were few (widely-spaced) but strong,
while during mild wave conditions rips were more weaker and more numerous
(closely-spaced). Bird (2000), and
others consider the return flow in the bays between a beach cusp series (in
what I call the zones of retarded flow (Gorycki, 1973) to be mini-rip systems.
These currents derive from the confluence and return to the sea of what I
suggest are the combined halves of fluid salients that fan out from adjacent
cusps. The currents would be of short duration, but recurrent, since they would
be produced by each wave of a size capable of cusp maintenance (Gorycki, 1973).
This contention agrees with the observation of Masselink (1999) that cusp
spacing is strongly related to the horizontal swash excursion. That is, waves
of equal strength engender, develop, and maintain a cusp series of a certain
spacing. These return flow currents between the cusps, and also the offshore
submarine deltas produced by them, will impede portions of the next incoming
wave and will help to evenly subdivide it so that those portions which do reach
the beach face become salients aligned with the cusps. Being of short duration,
mass, and length, and lacking defined longshore currents, these “rip
currents” should not have well-developed channels. Instead, the bay between the
cusps is the channel analogue, combined with associated submarine deltas. In
this case, the spacing between cusps should not be very much greater than the
zones of retarded flow (width of the bays) which lie between the cusps.
Masselink and Pattiaratchi (1998) would call this type of circulation pattern
horn divergent flow and also consider it to play a key role in forming and
maintaining beach cusp morphology. They suggest the regular spacing of beach
cusps varies from 10 cm to 40 m. However, they find that the swash flow
circulation pattern does not explain the actual formation of beach cusps or
their even spacing. I would suggest that these short-term periodic return flows
between beach cusps, where no longshore currents operate, should not be called
rip currents since they have already been defined as turbulent zones of
retarded flow (Gorycki, 1973) in which backrush is returned to the sea. Evenly spaced (approximately 100
m apart) rip currents have also been described as generated in quasi-periodic
holes in an alongshore bar. [3] http://www.oc.nps.navy.mil/~thornton/ripex/ripex.htm I would suggest that the
alongshore “bar” may simply be a series of submarine deltas generated by a
series of evenly spaced backrush from the bays of a large cusp series separated
by the locations of incoming salients. If the quasi-periodic “holes” become rip
current sites during a later wave regime and tide (water) level, they would
merely be expedient sites of return backrush at the scale and spacing of a
beach cusp series. BEACH CUSPS AND NEARSHORE
CIRCULATION CELLS Evenly spaced giant cusp
series have been described (Shepard, 1952; 1963) and measured as being from 150
m to 1000 m apart, with most spaced between 500 m and 600 m (Dolan, 1971).
Also, the cusps project an average of 15 m to 25 m seaward from the embayments.
For a modest situation involving a 25 m cusp length and a 500 m cusp spacing,
the ratio for giant cusps is I suggested (Gorycki, 1973) that during beach cusp formation,
the zones of retarded flow (return flow, or backrush in the bays), and
submarine deltas would be located midway between the cusps. It should be
noted that this backrush simply accommodates the mass of a single wave by
subdividing that wave into each bay of that cusp series. Some sediment could be
added to the cusps by incoming salients, but erosion of the bays by backrush in
the zones of retarded flow would be more effective to excavate the bays,
actively aid in the passive development of the cusps, vigorously form submarine
deltas and actively subdivide incoming waves. To understand the formation of a
series of giant cusps aligned with rip currents, I would emphasize that rips
are persistent components of beach dynamics, supported by a portion of each
incoming wave recurring over a lengthy section of beach face. Since large
volumes of incoming water support the longshore currents that feed the rips,
any transported sediment, excavated from the beach face, would be moved toward
the rips where the converging currents would then deposit it as cusps and then
move seaward to deposit submarine deltas. The combination of persistent rips,
heads and associated submarine deltas would then serve to subdivide incoming
waves to maintain the mechanism. Thus, the formation of an evenly spaced giant
cusp series, with rip currents in their lee, would result from strong, uniform
onshore winds producing a powerful wave regime. If this causes a voluminous
set-up and lateral migration of water acting on a uniform beach face, it would
produce rips of any uniform great spacing which would subdivide each incoming
wave, and supplant the concept of nearshore circulation cells. The disparity in
surf dynamics resulting in the generation of giant cusps as opposed to the formation
of a beach cusp series suggests that they should not be confused or even
compared. In my paper on the formation of beach cusps (Gorycki,
1973), I suggested that if wave conditions change, the normal variability of
wave size could be accommodated by established beach cusps in that smaller than
average waves would have little effect on established cusp systems. Masselink
and Pattiaratchi (1998) would describe this type of circulation pattern as
oscillatory. In the case of larger than average size waves, particularly if
associated with a rising tide, incoming waves would escape the retarding
effects of the submarine deltas and tend to passively and unimpededly
surge directly into the bays between the cusps (Gorycki, 1973). Backrush of
water spreading out within a bay would then tend to split symmetrically toward
the cusps on either side, possibly adding sediment to the cusps. Bird
(2000) would call these “rips” in the lee of the cusps, even though the
rips are short-lived, whereas Masselink and Pattiaratchi (1998) would more
correctly describe this type of circulation pattern horn convergent flow for
beach cusps. A prolonged or significant change in the wave regime would
eventually destroy a cusp series, including the submarine deltas, or at least
alter cusp spacing. Komar (1971), states that, “Both cusp-rip current
relationships appear to occur in nature.”, but proposes that rips in the lee of
cusps is the more likely situation and proposes that they be called “rip
cusps”. He also suggests that it is the development of back eddies which would
produce the rips seaward of the
cusps, but, “It is possible that in certain circumstances, such as on a steeper
beach face, the rips will hollow out embayments leaving cusps midway between
the rips.” For these, Komar merely proposes a lack of development of back
eddies in the bays so that cusps do not form at those locations and that the
cusps are at “positions of zero transport”, passively produced as the bays are
excavated. The point to be made here is that beach cusp formation requires that
salients be aligned with cusps, and return flow be between cusps. Cusps in the
lee of so-called “rips” (return flow), suggests either that salients are
passively aligned with bays, due to a horn convergent flow regime in a beach
cusp series, or that true rip currents are active and responsible for giant
cusp production. Komar (1971) does mention that some cusps he describes in
the field and in his laboratory studies should be classified as beach cusps,
based on their more closely spaced rip currents and small cusp spacing, but
still feels that since these are “associated with rip currents” they should be
called “rip cusps”. Additionally, Komar (1976)
states, “When wave crests are parallel or nearly parallel to the shoreline, the
nearshore currents are dominated by a cell circulation with seaward-flowing rip
currents. This cell circulation is produced by longshore variations in wave
breaker heights, which in turn produce longshore variations in the wave set-up.
The set-up will raise the water in the nearshore to high levels shoreward from
positions of large breakers than shoreward of smaller breakers. Water will then
flow alongshore toward locations of small breakers and set-up, converging and
turning seaward as a rip current. The rip currents transport sand offshore to
beyond the breaker zone, hollowing out embayments in the process. A series of
rip currents can thereby produce a series of embayments separated by cuspate
projections.” In response, I would contend that his small breaker portions,
small setup, eroded embayments, rip currents, and sand transported offshore
beyond the breaker zone, possibly to form submarine deltas, would then be
components of what I call zones of retarded flow for beach cusp formation, but
which are too widely spaced for that designation. These locally inhibit wave
approach and promote broad areas of “large breakers” between the rips, similar
to salients involved in beach cusp formation but which, again, are too large
for that designation. This structuring of incoming waves, determined by the rip
currents, rather than ...“longshore variations in wave breaker heights,”...
would be responsible for the so-called “cell circulation”. Komar’s (1971)
figure 1 portrays the typical condition of rips in the lee of giant
cusps which would be one in which broad incoming waves, contained and
defined by rip currents on either side are centered on the bays. His figure 2
shows his “envisioned” cuspate shoreline with rips in the lee of embayments,
but he ...“is uncertain whether such a development occurs in natural beaches.”
We should note that the large breaker portions and associated high levels of
water (high set-up) suggest overly large salients centered on cuspate
projections. These “salients” are confined between rip locations (zones of
retarded flow) on either side, and the general picture presented is what one
would observe during the formation of a beach cusp series. In Komar's (1971) discussion of
his laboratory experiments he states, “In all cases, it is found that
cusps develop in the lee of the rip currents.” In that paper, the first
of his wave basin experiments produced four cusps aligned with rip
currents. Subsurface channels, also aligned with the cusps, were excavated by
the rips, and extended away from the shoreline. Unfortunately, these
experimental runs had to be of short duration. I suggest that here wave action
was strong and horn convergent (Masselink and Pattiaratchi, 1998). Sediment
eroded from the bays by fluid salients would be transported to form cusps
(either actively or passively), and the seaward return flow in the lee of the
cusps was strong enough to excavate the subsurface channels. The second of Komar's wave basin
experiments at another laboratory initially produced rip currents midway
between cusps. These cusps were of short duration, followed by development
of three permanent cusps aligned with the rip currents. Here, a large
central cusp formed shoreward of a strong central rip and with a smaller cusp on
either side, each aligned with a weaker rip. Of interest here is that these
later cusps extend below the surface into deeper water as ridges rather than as
channels seen in the first experiments. Komar suggests this configuration is an
equilibrium condition because once these permanent cusps formed, all cell
circulation, sediment transport, and longshore and rip currents ceased to
exist. Komar also suggests that this equilibrium may be the reason why cusps
are not necessarily seen with rip currents in nature. Several problems are suggested by
Komar's second laboratory experiments. Longshore currents would require
a proportionately much greater distance between cusps of the size produced. The
cusps are spaced only about 5 m apart, which seems to suggest insufficient
space for longshore currents to develop and be active, and Komar, himself,
admits that his experimental forms look more like the typical natural beach
cusp series which he observed in the field. In the first phase of those
experiments, there might initially have been fluid salient deposition of cusp
material on the beach face as Masselink and Pattiaratchi's (1998) horn
divergent flow. The temporary cusps first formed midway between rip currents
(zones of retarded flow returning “seaward”) with concomitant erosion of bays
(and probable deposition of submarine deltas), between the cusps. This is what
I described above (Gorycki, 1973) for beach cusp series production, but
with the emphasis on the structuring of the incoming waves forming evenly spaced
fluid salients aligned with the cusps. The return flow (the so-called rips
between cusps) would then cause erosion and development of the embayments
between cusps and, in combination with the deposited submarine deltas, would
tend to structure the next wave so that salients would again be aligned with
the cusps. In support of this, Komar does suggest that it “...is possible that
in certain circumstances, such as on a steeper beach face, the rips will hollow
out embayments leaving cusps mid-way between the rips.” Komar shows the beach
configuration after two hours of operation of his second experiment (his figure
3). Initially, displaced sediment carried out to deep water to form submarine
ridges between the early-formed cusps would then inhibit incoming waves at
those locations and thus align incoming fluid salients with those short-lived
cusps. Continued wave action then resulted in subsequent erosion of the
early cusps to form bays, assumedly at the former cusp locations, with
concomitant deposition of later cusp material both on the beach and continuing
as the ridges below the water surface. These ridges are aligned with the rip
currents. Again, the erosion of the early cusps to form bays would result from
wave action being confined to regions between the submarine ridges. Headward
erosion of these bays would result in intervening, developing cusps becoming
aligned with and continuing seaward as ridges. As stated previously, Komar
suggests an equilibrium condition prevailing in the experiments in which these
permanent cusps persist over hours of continuous wave action, and that all cell
circulation, sediment transport, and longshore and rip currents cease to exist.
To explain this situation, as I suggested earlier, a normal variability of wave
size could be accommodated by natural beach cusp systems (Gorycki, 1973). The
wave basin experiments described here seem to offer no chance for the
expression of the effects of a spectrum of wave sizes seen in nature. The point
to be made here is that, in these second experiments, the shoreline has become
more complex. There is the development of cusps, bays, submarine deltas,
submerged cusp extensions (submarine ridges) and other changes in the bottom
topography and beach face, including the erosional transition from a steep to a
more gentle beach face, which may have promoted the erosion of the early cusps.
Consequently, there is also a gradual lengthening of the shoreline and a
greater distance from wave generator to that eroding shoreline. All these
changes would eventually have a weakening effect on the identical, mechanically
produced waves in the system. As described earlier, smaller than average waves
would have little effect on established cusp systems. This gradual sapping of
uniform wave energy against a more complex shoreline, resulting in Komar's
“equilibrium condition”, would then have a deleterious effect on the
experiments and the resulting observations and conclusions. I would also like to point out
that the production of only three cusps in Komar's second wave basin
experiments strongly suggests a wall effect on the dynamics of the water
motion. That is, a larger central cusp bounded by adjacent weaker cusps
indicates the basin's sidewalls may artificially aid in structuring and
weakening the incoming waves. I would prefer to see four or more identical
cusps being produced. In the case of my tilting trough experiments, anywhere
from six large to more than twelve smaller fluid salients were routinely
produced with each flow of water across the width of the trough's bottom,
without any influence of a wall effect in the central region of the trough. The
problem of experimentally introduced artifacts of fluid structuring has been
previously described in my earlier web site [1]. For instance, Faller's (1978)
wind and wave tank employed to produce Langmuir circulation cells
experimentally generates a regular pattern of crossed waves created by a double
wedge that oscillates vertically at a resonant frequency. An exhaust fan at the
far end of the tank also draws a light wind over the waves as they move along
the length of a long, narrow tank. A transparent wind shield, which lies close
to the water surface, induces the moving air to act on the waves. In 20
seconds, the combination of waves and wind causes: 1) scattered floats to align
into two lanes parallel to the tanks walls, and 2) two fluid salients of clear
water, moving in the direction of the wind, to displace dye at the tank's
bottom. Faller suggests that this combination of events indicates proof of the production
of Langmuir circulations, with two pair of longitudinal roll vortices operating
in the water of the tank. However, Langmuir's (1938) own careful observations
provide evidence that suggests that it is the formation of fluid salients in
the wind above a water surface, which is the mechanism responsible for the
appearance of the so-called Langmuir circulation cells in the water. The
assumed cylindrical cells, only sketched by later workers, do not comply
with Langmuir’s own detailed description of unexpectedly shallow, near surface
circulation patterns, which he observed during his experiments on Lake George
[1]. Describing “helical vortices” in the waters of In Faller's experiment, I would
suggest that there is also a wall effect (as described here for Komar's (1971)
experimental study of rip currents) and that the symmetry of the oscillating
wedge is reflected in that of the paired water salients and lines of floats. I
would prefer to see the production of four or more water salients with
superimposed float alignments and waves created by a simple paddle to
obviate any suggestion of the influence of a wall or wedge effect. BEACH CUSPS AND EDGE WAVES Some researchers have suggested
that edge waves are responsible for the production of beach cusps. A discussion
of standing edge wave theory describes a complicated interaction between an
incoming wave (parallel to the shore) and a pair of edge waves set up
perpendicular to the shoreline and approaching each other. These standing edge
waves near the shoreline form a series of nodal and antinodal points. The
antinodal points define alternating peaks and troughs; the nodes, points where
there is no vertical motion. If the incoming wave collides with a peak, there
is an increase in height and greater erosion; if with a trough, a decrease in
height and erosive ability to the wave. If the incoming wave has the same wave
period as the edge wave, they are termed synchronous and are considered
uncommon. If the standing edge waves have a wave period twice that of the
incoming wave they are considered subharmonic, resulting in a regularly spaced
series of and troughs along the incoming wave and it is these that are
considered responsible for the development of a beach cusp series. The problem
with this theory is that it accounts only for the initiation of beach cusps,
and not their continued growth since the amplitude of the edge wave decreases
as the size of the cusps increase. In comparison to this theory, the fluid
salient mechanism is a simpler, easily demonstrated, and more readily
understood explanation for beach cusp initiation, formation, and maintenance. Komar (1971) describes the waves (his
figure 5) at the points of cusps as being appreciably smaller than waves
present in the embayments on either side throughout his experiments, remaining
so even after equilibrium had been achieved. He suggests that this indicates
the presence of edge waves that are instrumental in producing the cell
circulation with the rip currents developing in the positions of the lowest
breakers. I, again, would suggest that in these experiments deposited sediment,
continuing from the cusps as ridges below the water surface, would effectively
serve to diminish any wave activity locally approaching the cusps, leaving
stronger waves to break in the bays. Masselink (1999) rules out the edge wave
mechanism of beach cusp formation of Guza and Inman (1975) because he could
find no relationship between cusp spacing and beach face gradient. In addition,
Inman and Guza (1982) conclude, “...that swash cusps are formed by the swash
and backwash acting directly on the beach face...” They rely on edge waves
“...only to provide small periodic perturbations on an originally uniform
beach... but felt the edge waves ...need not persist for the development of
mature cusp morphology.” That is, as cusps increase in size, the amplitudes of
edge waves correspondingly decrease. Inman and Guza’s edge waves, which produce
“small periodic perturbations on an originally uniform beach”, could also be
described as fluid salients. Werner and Fink (1993) also find that since
“...subharmonic edge waves decay strongly within one incident wavelength of the
shore, they are difficult to detect.” Edge waves have been treated in a number of theoretical
discussions and also variously described as; 1) ...“invisible-to-the-eye,
ankle-to calf-high waves that extend from intermediate depths on the
continental shelf to the shoreline (where they are highest) and travel along
the coast”... [4] http://skagit.meas.ncsu.edu/~drake/drake/abstracts/Science285_Drake_review.html, 2) ...“ocean waves traveling parallel to a shore with crests
normal to the shoreline, and having heights that diminish rapidly seaward and
are negligible at a distance of one wavelength offshore”... (Beer, 1997, p.
75-76), 3) ...“often difficult to visualize, are coastally trapped, i.e. their
amplitude is maximal at the shoreline and decays rapidly offshore, produce on
the beach beautiful run-up patterns (highest points reached by a wave on the
beach”... [5] http://arxiv.org/pdf/physics/0106086, 4) ...“being produced
perpendicular to normally incident waves and which can produce nodal and
antinodal points which are responsible only for cusp initiation”... [6] http://en.wikipedia.org/wiki/Beach_cusps,
5) ...“water waves that are
trapped at the shoreline by refraction”..., [7] http://www.coastal.udel/faculty/rad/edgetheory.html
Because of these varied
descriptions (occasionally accompanied by supportive sketches), and the
preceding discussion, edge waves do not seem a viable explanation for beach
cusp periodicity. As an aside, edge waves become a
problem in the manufacture of metal foils. Waves form on the edges of the sheet
as a foil thins during rolling because its unsupported edges suffer a more
intense compression and thinning. A more familiar version of edge waves is
produced by tearing a heavy (5-mil) sheet of polyethylene plastic as one would
normally tear a sheet of paper. To start the tear, it is best to initiate it by
first making a small cut with a scissors. Interestingly, the sheet not only
exhibits a uniform series of large edge waves (primary salients) a few mm from
the edge but also a uniform series of smaller, secondary edge waves at the torn
edge, (Fig. 4); both sets are caused by tension and thinning along the tear. Fig.
4. Primary edge waves approximately 4 mm in wavelength near the torn
edge of a 5-mil thick polyethylene plastic sheet. Secondary edge waves at
the edge of the sheet are also visible and are about 1 mm apart. The waves form
due to compensatory lateral compression after initial tensional thinning as the
edge is being torn. Evenly spaced salients similarly form in fluids as the
result of extension/compression. The fluid salient mechanism often presents as
a series of primary, secondary, tertiary and even higher orders of waves in
other phenomena. The point to be made here is that
these edge waves have nothing to do with standing edge wave theory, but are
obviously produced by an (axial) extension of material near the tearing edge,
along its length, just as described here for the formation of fluid salients.
The waves may be reduced or eliminated by stretching the film in a direction
parallel to its edge. The rolling between plate glass of the rubber cylinder
physical model described in my first web site [1] also produces a uniformly
repeated wave pattern created by extension of the cylinder along its axis. As a consequence of this
discussion, I suggest that edge waves, when actually photographically
depicted as being responsible for cusp formation on the beach face (or as
“mini-rips”), are in fact fluid salients which are generated by axial extension
of individual waves, as the waves are interacting with the beach face (Gorycki,
1973). Salients moving toward the shore provide the mechanism for the
production, maintenance and, especially, the even spacing of beach cusps. BEACH CUSPS AND THE
SELF-ORGANIZATION MODEL Werner and Fink (1993) describe a
computer simulation of flow and sediment transport in the swash zone that
couples local flow acceleration and alongshore surface gradient. They present a
simulated cusped beach developed after 250 computer generated swash cycles.
This image is not dissimilar to my sediment-strewn rocking trough pattern after
one swash cycle (again, see Fig. 3) which reiterates Evans’ (1938) observation
of the formation of cusps on a beach as the result of the action of a single
wave. However, Werner and Fink find that current observational data cannot
determine whether their self-organization model or the standing edge
wave model is responsible for the formation of beach cusps. Interestingly, they
imply a passive role to swash stating that, “On a cuspate beach, runup
is deflected by horns toward bays and from there flows seaward as runout.” Masselink (1999) finds the strong
relationship between cusp spacing and horizontal swash excursion to provide some
support for the self-organization model of beach cusp formation. This supports
my suggestion (Gorycki, 1973) that, “... the increase in salient size and
spacing with distance traveled in the experimental situation might suggest that
the further swash extends up the beach face, the greater the intercusp
spacing.” Since Masselink (1999) also could not find any correlation between
cusp spacing and the gradient of the beach face, this implies that for any
slope, the larger the waves, the greater the cusp spacing. Masselink et al. (1998) also
describe the destruction of the lower portion of a beach face during a small
storm and the reappearance of a cusp series, “...under the influence of
declining wave conditions...” Interestingly, they find the cusps redeveloped at
the same locations and with the same dimensions as the subtle remnants of the
cusp series on the upper beach face and feel this observation supports the
self-organization model of Werner and Fink (1993) because the cusp reformation
was controlled more by the antecedent morphology than by the hydrodynamic
conditions. They also find that the positive feedback between swash
hydrodynamics and beach face morphology, necessary to form beach cusps, does
not require a large variation in relief. I find that these observations by
Masselink et al. (1998) strongly support the operation of the fluid salient
mechanism and my earlier conclusions (Gorycki, 1973) that salients would become
aligned with, and enhance cusps on the beach face if submarine deltas are present
seaward of the bays. The deltas would act to inhibit wave action at those
locations under “...declining wave conditions...”, and would register the
intervening salients with the subtle remnants of cusp locations on the upper
portion of the beach face. This would occur even though the lower
portion of the beach face was destroyed and the cusp remnants there, if any,
had no influence on the incoming swash. Moreover, the swash (salients) would
diverge at the former locations of forming cusps and return seaward as
zones of retarded (return) flow, excavating the intervening bays and adding
material to enhance the submarine deltas. If swash excursion is responsible for
cusp spacing, and wave energy is responsible for the swash, we also might want
to look seaward for the mechanism responsible for the spacing: not only the
evenly spaced return flow and the enhancement of submarine deltas, but the
cusp-initiating fluid salient mechanism as well. Coco et al. (2003) also find that
their field observations of swash flow patterns and morphology changes are in
agreement with the self-organization hypothesis. They suggest that the
formation and development of beach cusp morphology is associated with waves
normally approaching the shoreline (Longuet-Higgins and Parkin, 1962;
Sallenger, 1979; Guza and Bowen, 1981). Others take a less severe view.
Rudowski (1964), Evans (1938), Guilcher (1950), and Kuenen (1948) find that
cusps can be formed by waves that approach the beach at an angle. In support of
this, the rubber cylinder model can produce salients even when the upper glass
plate is moved at an acute angle to the axis of the cylinder (Fig. 2). This
observation accommodates the possibility that waves approaching other than
strictly parallel to the shore may be capable of producing cusp-generating
salients. Coco et al. (2003), in a
discussion of observations and experiments at Duck, Again, the statement by Coco et
al. (2003) that, “...swash is diverted from incipient horns to incipient bays,
leaving residual deposition on horns and leading to enhanced erosion in bays”,
implies an initial periodicity to the beach face relief that provides a
template for the swash locations to develop and enhance the future cusps. Any
other kind of relief would have to be reworked and refined by the swash, so
that a series of cusps of varying spacings would give way to a uniform series.
This again suggests that the swash has its own initiating structural
periodicity. Furthermore, if cusp-centered swash continues upbeach and becomes
diverted toward the bays where its return is impeded by scouring of the bays
and seaward sediment transport, this too suggests operation of the fluid
salient mechanism as the return flow in the bays subdivides the next incoming
wave (Gorycki, 1973). From this
initializing spacing, the development, maturation, and permanence of a cusp
series could then follow as previously described. Excellent photos of beach
cusps comprised of sediment coarser than the beach average, subaqueous deltas,
fluid salients, zones of retarded flow, and multiple cusp series on the [8] http://kootenay-lake.ca/waterworld/beach/beachcusps/index.html
provide revealing images of the
fluid salient mechanism that are easily visualized because of their small scale
and the absence of intrusive detail. Coco et al. (2003) also find three
signatures of self-organization in beach cusp formation: “First, time lags
between swash front motions in beach cusp bays and horns increase with
increasing relief, representing the effect of morphology on flow. Second,
differential erosion between bays and horns initially increases with increasing
time lag, representing the effect of flow on morphology change because positive
feedback causes growth of beach cusps. Third, after initial growth,
differential erosion decreases with increasing time lag, representing the onset
of negative feedback that stabilizes beach cusps.” It should be noted that the
first of these signatures could also be attributed to the operation of fluid
salients mechanisms wherein the swash’s effect on morphology induces an
increased time lag. The second signature
relating time lags to differential erosion between bays and horns is in keeping
with the fluid salient mechanism. Here, the waves approaching the beach face
would already be predisposed to have the same salient structure, spacing and
locations as the cusps already produced by the salients of the previous wave’s
swash. The resulting enhanced morphology could then be considered responsible
for the increased time lag of the swash.
The third signature relating a further increase in time lag
to the onset of negative feedback that stabilizes beach cusps would relate back
to Komar's (1971) “equilibrium condition”. The development of submarine deltas
and other changes in the bottom topography and beach face, including the
development of steeper (cusp) and more gentle (bay) slopes, and a gradual
lengthening of the shoreline due to cusp and bay formation, would all serve to
dissipate the energy of uniform, incoming waves so that the beach face becomes
stabilized. What should be mentioned in the third signature is that the
material eroded from the bays would be deposited as submarine deltas that, in
combination with the enhanced shoreline morphology, would also serve to
dissipate the energy of incoming waves, leading to, and promoting, an “equilibrium
condition”. The gradual waning of wave energy during the period after the storm
would also aid in stabilizing a cusp series. At Duck, even if waves did not
initially physically register with the cusps on the upper beach face, it would
appear that with waning storm conditions, submarine deltas, centered on the
bays, would eventually act to slow those portions of incoming waves. Salients
would then approach the pre-storm cusp locations to continue the cycle,
reestablish, and enhance the cusp series. Submarine deltas, offshore
dynamics and the structuring of incoming waves tend to be ignored in many
discussions of beach cusp formation. It should be noted that the Duck
experiments do not appear to include a comprehensive surveying of the submerged
portion of the beach, only bulldozing and surveying of the preexisting cusps on
the beach face. This region is defined as the, “section of the beach normally
exposed to the action of the wave uprush” (Glossary of Geology and Related
Sciences, 1957, p. 27). Also, only three cusps were bulldozed, and the cusps on
either side, especially along with their submarine deltas, might also have
served to help register fluid salients with the missing cusps. Storms tend to
raise sea level temporarily, and this may allow submarine deltas to escape
destruction. With waning conditions, the deltas would reassert their
structuring of waves so that fluid salients may regenerate destroyed cusps at
their former locations. If the self-organization model were in effect, one
might expect that reforming cusps might not necessarily be in register with
their former locations; nor would they necessarily have the same spacing (and
numbering) throughout their formational history. CONCLUSIONS In this and
other fluid salient phenomena, I suggest that structuring of the moving fluid
is the primary morphological determinant, whereas sediment plays a passive
role. As a consequence, contradictory statements by others that relate to the
role of sediment in beach cusp formation might be reconciled. The role attributed
to edge waves in simply initiating cusp periodicity seems tenuous at
best. The self-organization model, while detailed and descriptive, does not
resolve the problem of the periodicity of cusp spacing except to relate
it to swash excursion. The importance of submarine deltas and zones of retarded
flow as swash returns to the sea should be acknowledged as to the effects they
have on salient spacing and cusp morphology. Additionally, the apparent action
of the fluid salient mechanism in a variety of other phenomena [1] supports the
likelihood of the generation of fluid salients on the beach face and their
influence in the production of beach cusp series. The analysis
by Coco et al. (1999) of field and laboratory data collected over the past 50
years suggested a possible link between both edge waves and swash-sediment
feedback for beach cusp formation. These theories can now be replaced by a
single theory that not only provides for cusp series initiation, uniform spacing,
and development, but for a number of other periodic structures in nature and in
the laboratory. Consequently, I feel the answer to the cause of beach cusp
formation is the fluid salient mechanism. FINAL COMMENTS My original paper, discussing the
mechanism for beach cusp spacing (Gorycki, 1973), was precipitated merely by
noting the uniformly spaced scalloped edge of a sheet of water traversing the
bottom of a small tray as it is tilted. I called this structuring sheetflood,
defined as “...pure water...flowing... on an indestructible surface...tends at
first to divide into parallel streams...” (Glossary of Geology and Related
Sciences, 1957, p. 263). However, I now feel it is just another version of the
fluid salient mechanism that can operate in a number of disparate phenomena and
under a variety of guises. This web site is the first of a
series presenting further comments and information described in my original web
site [1]. Questions,
comments and criticism are welcomed and may be addressed to me at:
[email protected] REFERENCES Beer, T.,
1997, Environmental Oceanography, CRC Press, 367 p. Bird, E., 2000,
Coastal Geomorphology, Wiley International, Coco, G., Burnet, T. K., Werner,
B. T., and Elgar, S., 2003, Test of Self-Organization in Beach Cusp Formation:
Jour. Geophys. Res., v. 108, no. C3. Coco, G., O’Hare, T. J., and
Huntly, D. A., 1999, Beach Cusps: A Comparison of Data and Theories for Their
Formation: Jour. Coastal Res., v. 15, no. 3, p. 741-749. Dolan, R., 1971, Coastal
Landforms: Crescentic and Rhythmic: Geol. Soc. America Bull., v. 82, p.
177-180. Evans, O. F., 1938, Classification
and Origin of Beach Cusps: Jour. Geology, v. 46, p. 615-627. Faller, A. J., 1978, Experiments
with Controlled Langmuir Circulation: Science, v. 201, p. 618-620. Glossary of Geology and Related
Sciences, 1957, American Geological Institute, Gorycki, M. A., 1973, Sheetflood
Structure: Mechanism of Beach Cusp Formation and Related Phenomena: J. Geol.,
v. 81, p. 109-117. Guilcher, A., 1950, Observations
sur le Croissants de Plage: Soc. Géol. France (5), v. 19, p. 15-30. Guza, R. T., and Bowen, A. J.,
1981, On the Amplitude of Beach Cusps: J. Geophys. Res., v. 86, p. 4125-4132. Guza, R. T., and Inman, D. L.,
1975, Edge Waves and Beach Cusps: J. Geophys. Res., v. 80, p. 2997-3012. Inman, D. L., and Guza, R. T.,
1982, The Origin of Swash Cusps on Beaches: Mar. Geol., v. 49, p. 133-148. Johnson, D. W., 1919, Shore
Processes and Shoreline Development, New York, Wiley, 584p. Komar, P. D., 1971, Nearshore Cell
Circulation and the Formation of Giant Cusps: Geol. Soc. America Bull., v. 82,
p. 2643-2650. Komar, P. D., 1976, Beach
Processes and Sedimentation, Prentice-Hall, Kuenen, Ph. H., 1948, The
Formation of Beach Cusps: Jour. Geology, v. 56, p. 34-40. Langmuir, I., 1938, Surface
Motion of Water Induced by Wind: Science, v. 87, no. 2250, p. 119-123. Longuet-Higgins, M. S, and
Parkin, D. W., 1962, Sea Waves and Beach Cusps: Geogr. J., v. 128, p. 194-200. Masselink, G., 1999, Alongshore
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Processes and Landforms, v. 24, p. 335-347. Masselink, G., Hegge, B. J., and
Pattiaratchi, C. B., 1998, Beach Cusp Morphodynamics: Earth Surface Processes
and Landforms, v. 22, p. 1139-1155. Masselink, G., and Pattiaratchi,
C. B., 1998, Morphological Evolution of Beach Cusps and Associated Swash
Circulation Patterns: Marine Geology, v. 146, p. 93-113. McKenzie, R, 1958, Rip Current
Systems: J. Geol., v. 66, p. 103-133. Palmer, H. R., 1834, Observations
on the Motions of Shingle Beaches: Royal Soc. (London) Philos. Trans., v. 124,
p. 567-576. Rudowski, S., 1964, Beach Cusps
on the Polish Coast of the Baltic (Summary): Acta Geologica Polonica, v. 14, p.
147-153. Sallenger, A. H., 1979, Beach
Cusp Formation: Mar. Geol., v. 29. p. 23-37. Shepard, F. P., 1952, Revised
Nomenclature for Depositional Coastal Features: Am. Assoc. Petroleum Geologists
Bull., v. 36, no. 10, p. 1902-1912. Shepard, F. P., 1963, Submarine
Geology, 2nd ed.: New York, Harper and Row, 557 p. Shepard, F.
P., and Inman, D. L., 1951, Nearshore Circulation: 1st Conf. Coastal Engr.
Proc., p. 50-59. Werner, B. T., and Fink, T. M.,
1993, Beach Cusps as Self-Organized Patterns, Science, v. 260, p. 968-970. WEB SITES [1] http://www.geocities.com/magsalients/ [2] http://news.ufl.edu/2000/research/engineering/2000/ [3] http://www.oc.nps.navy.mil/~thornton/ripex/ripex.htm [4] http://skagit.meas.ncsu.edu/~drake/drake/abstracts/Science285_Drake_review.html [5] http://arxiv.org/pdf/physics/0106086 [6] http://en.wikipedia.org/wiki/Beach_cusps [7] http://www.coastal.udel/faculty/rad/edgetheory.html [8] http://kootenay-lake.ca/waterworld/beach/beachcusps/index.html You are visitor number: 
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